Breathers for nonlinear energy management in acoustic waveguides

Abstract

Recent investigations of nonlinear metamaterials have revealed interesting wave propagation phenomena with no counterpart in linear systems. One of the appealing phenomena is traveling discrete breathers. Breathers are traveling oscillatory wavepackets with spatially localized envelopes and energy-dependent speeds. These nonlinear waves were reported in lattices with purely (or nearly purely) nonlinear neighbor interactions (possessing zero speed of sound as defined in the classical acoustics sense, and, hence, designated as sonic vacua). However, the effect of local resonators on breather propagation is elusive to date. In this work, we aim to fill this gap by studying 1D grounded strongly nonlinear lattices with linear local resonators (SNLRMs) under impulsive force excitation. Numerical simulations have demonstrated that SNLRMs support the generation of new families of breathers. These families resulted from the opening of a new optical propagation zone (PZ) in the spectrum, which is associated with the linear dynamics of the local resonators. These families are characterized by the local resonator parameters and can support multiple fast frequencies or a single frequency that belongs to either the optical or acoustical PZs. Further aspects of the nonlinear acoustics are also demonstrated using the complexification averaging method. The newly reported breathers open the venue to employ SNLRMs in passive nonlinear energy management applications. Examples are presented through acoustics waveguides and frequency filtering.